The present embodiments relate to electrostatic transducers (i.e., capacitive micro-machined ultrasound transducers (CMUTs)).
An element of a CMUT transduces between electrical and acoustic energy. The element includes a plurality of membranes 12 (see FIG. 1) formed on a silicon substrate 14. Each membrane 12 is adjacent a single gap 16. An electrode is adjacent to the membrane 12, and another electrode is on the other side of the single gap 16. A DC voltage applied to the electrode adjacent the membrane 12 biases the membrane 12. Variation in electrical potential between the electrodes causes the membrane 12 to flex into and out of the gap 16. The flexing generates acoustic energy. Acoustic reflections cause the membrane 12 to flex, causing variation in electrical potential.
The force on the membrane 12 may be represented by:
      F    =                            ɛ          0                ·        Area        ·                              (                                          V                dc                            +                              V                ac                                      )                    2                            2        ⁢                              (                          d              -              w                        )                    2                      ,where Vdc is the DC bias voltage, ε0 is a constant representing the permittivity of free space, Vac is the AC voltage signal, d is an initial gap or separation, and w is the AC displacement from an equilibrium position. The membrane displacement, which determines the output pressure, responds proportionally to the force at low frequencies. An estimate of nonlinear distortion is possible by analyzing the equation above for electrostatic force. The voltage-squared term in the numerator dominates the nonlinear distortion since the AC displacement, w, is usually much smaller than the total gap distance, d. Second harmonics are generated, and are roughly proportional to the ratio of Vac/Vdc for small AC displacements (i.e., w<<d). Second harmonics generated by a transducer may be undesired, especially in imaging modes that attempt to isolate 2nd harmonics generated in tissue or by contrast agent microbubbles. CMUTs designed for high pressure output can have AC displacements that are significant fractions of the nominal gap thickness. In this case, there will be additional nonlinear terms that produce both even and odd harmonics.
As the membrane 12 deflects and the spacing between capacitor plates (i.e., electrodes) reduces, the electrostatic force increases. At some amount of displacement, the electrostatic force overwhelms the restoring spring force of the membrane 12, causing the membrane to contact the substrate and hindering further movement. When parallel, rigid plates are assumed with a linear membrane restoring force, this distance is about ⅓ of the moveable gap 16 at low frequencies. This often restricts the maximum DC bias voltage and AC drive voltages that can be applied to the CMUT.